What are the rules and protocols of US presidential press conferences?

Question

This is not partisan. I want to know, what are the protocols and rules that decide which reporter is allowed and selected to make a question, how long in time the question must extend, and specially if the president, or another individual can:

1. Reject a question without even answering it.
2. Only choose questions from a non representative sample of reporters in the political spectrum.

Can the president accept from CNN, not MSNBC and yes FOX? Do every reporter get the same number of questions? Do reporters have to "fight" for the microphone to ask a question? Does just the president point to one of the reporters and receive their question?

Answer 1

There were no written rules until November 18, 2018. After Jim Acosta's refusal to yield the floor to another journalist despite his multiple questions being answered, his "hard" press pass (meaning he didn't have to show credentials) was revoked. US District Judge Timothy Kelly ordered the White House to reverse its decision on Fifth Amendment grounds, ruling that Acosta's due-process rights, or his chance to appeal the White House's decision, were violated. This was mainly due there being no written rules or guidelines.

In response, the White House re-instated Acosta's hard press pass and created a written policy. The White House stated that breaking any of these rules could result in the hard press pass being revoked.

The following rules were released on November 18th:

1. A journalist called upon to ask a question will ask a single question and then will yield the floor to other journalists.
2. At the discretion of the president or other White House personnel taking questions, a follow-up question or questions may be permitted; where a follow-up question has been allowed and asked, the questioner will then yield the floor.
3. ‘Yielding the floor’ includes, when applicable, physically surrendering the microphone to White House staff for use by the next questioner.
4. Failure to abide by any of these rules (1)-(3) may result in suspension or revocation of the journalist’s hard pass.

There is no rule about which journalist is called upon. The Press Secretary is Sarah Sanders. She typically tries to take questions from as many journalists as possible.

There is no time limit, although I imagine other journalists would get rather testy if someone took up the majority of the press conference asking a question.

Answer 2

The short answer, according to Ken Walsh here, "every president makes the rules of engagement, and the media play by them or get shunted aside."